The present invention relates to a performance analysis method, and more particularly to a performance analysis method of centrifugal impeller adapted to simply analyze the effect of centrifugal impeller.
Generally, rotating parts such as impeller and the like differ in performance thereof according to distribution of flow angle at blade exit, total pressure ratio, efficiency and the like.
Various physical quantity, design base of fluid machines such as impellers and the like, is obtained through three-dimensional flow analysis made on a base of certain turbulence state, through which performance is analyzed.
Among various impellers, a centrifugal impeller is composed of a disc-shaped base plate 50 and a plurality of blades 51 perpendicularly fixed to the base plate 50 and formed to have a certain curvature.
When the centrifugal impeller thus constructed is rotated, fluid is discharged from exit side (E) of the blade 51 bent at the predetermined curvature for blowing.
A centrifugal impeller manufactured in the above method according to a predetermined design dimensions is inspected for analysis of its performance, where an analyzed values thereof are generally exit flow angle, total pressure ratio, efficiency and the like.
At this time, the exit flow angle (xcex12m) which is a characteristic numerical value of the centrifugal impeller is defined by the following Formula 1, while, the total pressure ratio (PR) is obtained by Formula 2. The efficiency (xcex7s) is represented by formula 3.
Formula 1       α          2      ⁢      m        =            tan              -        1              ⁢          xe2x80x83        ⁢          (                        V          u2m                          V          m2m                    )      
Vu2m: absolute velocity in tangent direction at impeller exit side,
Vu2m=(1xe2x88x92"khgr")Vu2j+"khgr"Vu2w 
Vm2m: absolute velocity in radial direction at impeller exit side,             V      m2m        =                  b        -                                            b              2                        -                          4              ⁢                              xe2x80x83                            ⁢              a              ⁢                              xe2x80x83                            ⁢              c                                                  2        ⁢        a                  a    =                  m                  π          ⁢                      xe2x80x83                    ⁢                      D            2                    ⁢                      xe2x80x83                    ⁢                      b            2                              +                        r          +          1                          2          ⁢          r                          b    =                                        P                          2              ⁢              j                                ⁢                      xe2x80x83                    ⁢                      A            g                                    π          ⁢                      xe2x80x83                    ⁢                      D            2                    ⁢                      xe2x80x83                    ⁢                      b            2                              +                        m                      π            ⁢                          xe2x80x83                        ⁢                          D              2                        ⁢                          xe2x80x83                        ⁢                          b              2                                      [                                                            (                                  1                  -                  x                                )                            ⁢                              xe2x80x83                            ⁢                              V                m2j                                      +                          ϰ              ⁢                              xe2x80x83                            ⁢                              V                m2w                            ⁢                              
                            ⁢              c                                =                                                                      m                                      π                    ⁢                                          xe2x80x83                                        ⁢                                          D                      2                                        ⁢                                          xe2x80x83                                        ⁢                                          b                      2                                                                      ⁡                                  [                                                            R                      o2m                                        -                                                                                            r                          -                          1                                                                          2                          ⁢                          r                                                                    ⁢                                              xe2x80x83                                            ⁢                                              V                        u2m                        2                                                                              ]                                            ⁢                              
                            ⁢                              P                                  2                  ⁢                  m                                                      =                                                                                                      P                                              2                        ⁢                        j                                                              ⁢                                          xe2x80x83                                        ⁢                                          A                      g                                                                            π                    ⁢                                          xe2x80x83                                        ⁢                                          D                      2                                        ⁢                                          xe2x80x83                                        ⁢                                          b                      2                                                                      +                                                                            m                                              π                        ⁢                                                  xe2x80x83                                                ⁢                                                  D                          2                                                ⁢                                                  xe2x80x83                                                ⁢                                                  b                          2                                                                                      ⁡                                          [                                                                                                    (                                                          1                              -                              x                                                        )                                                    ⁢                                                      xe2x80x83                                                    ⁢                                                      V                            m2j                                                                          +                                                  ϰ                          ⁢                                                      xe2x80x83                                                    ⁢                                                      V                            m2w                                                                          -                                                  V                          m2m                                                                    ]                                                        ⁢                                      
                                    ⁢                                      V                                          2                      ⁢                      m                                                                                  =                                                                                          (                                                                        V                          m2m                          2                                                +                                                  V                          u2m                          2                                                                    )                                                              1                      /                      2                                                        ⁢                                      
                                    ⁢                                      T                                          2                      ⁢                      m                                                                      =                                                                            T                      o2m                                        -                                                                                            r                          -                          1                                                                          2                          ⁢                          r                          ⁢                                                      xe2x80x83                                                    ⁢                          R                                                                    ⁢                                              V                                                  2                          ⁢                          m                                                2                                            ⁢                                              
                                            ⁢                                              ρ                                                  2                          ⁢                          m                                                                                                      =                                                                                                              P                                                      2                            ⁢                            m                                                                                                    RT                                                      2                            ⁢                            m                                                                                              ⁢                                              
                                            ⁢                                              T                        o2m                                                              =                                          xe2x80x83                                        ⁢                                                                                                                        (                                                          1                              -                                                              xe2x80x83                                                            ⁢                              x                                                        )                                                    ⁢                                                      xe2x80x83                                                    ⁢                                                      T                            o2j                                                                          +                                                  xe2x80x83                                                ⁢                                                  xT                          o2w                                                +                                                  xe2x80x83                                                ⁢                                                                                                            r                              -                              1                                                        rRm                                                    ⁢                                                      xe2x80x83                                                    ⁢                                                      (                                                                                          W                                df                                                            +                                                              xe2x80x83                                                            ⁢                                                              W                                rc                                                            +                                                              xe2x80x83                                                            ⁢                                                              W                                lk                                                                                      )                                                    ⁢                                                      
                                                    ⁢                                                      P                            o2m                                                                                              =                                                                        P                                                      2                            ⁢                            m                                                                          ⁢                                                  xe2x80x83                                                ⁢                                                                              (                                                                                          T                                o2m                                                                                            T                                                                  2                                  ⁢                                  m                                                                                                                      )                                                                                r                            /                                                          (                                                              r                                -                                1                                                            )                                                                                                                                                                                                                  
Formula 2   PR  =            P      o2m              P      o1m      
Po2m: total pressure at impeller exit side
Po1m: total pressure at impeller entry side
Formula 3       η    s    =                    PR                                            r              -              1                        r                    ⁢                      xe2x80x83                              -      1                                T          o2m                          T          o1m                    -      1      
where, variable values in the above Formulae 1, 2 and 3 are
"khgr": wake area mass ratio (mw/m)
r: specific heat ratio
To2m: temperature at impeller exit side
To1m: temperature at impeller entry side
Ag: impeller exit area excluding blade thickness
m: mass flow
P: pressure
R: gas constant
V : absolute velocity
W: work ratio
D2: diameter at impeller exit
b2: exit width of impeller
where, subscripts are
0: total condition
2: impeller exit
2m: mixed condition
df: disc friction
j: jet
lk: leakage
m: radial direction
rc: recycling
u: tangent direction
Flow analysis utilizing Formulas such as above is obtained by substitution of numerical values to turbulence modeling defined in numerical expression relative to certain turbulence. At this time, a slip coefficient is introduced with a completely-mixed average flow speed relative to entire exit as standard while a manufactured impeller is activated to obtain an absolute exit flow speed. A flow angle against the absolute exit flow speed is then calculated to analyze the performance of the impeller.
However, there is a problem in the repeated performance analysis according to existing analysis method based on the completely-mixed average flow speed relative to the entire exit thus described in that the manufactured impeller has no optimum turbulence modeling to necessitate a plurality of turbulence modeling optimized to various parts of the impeller, complicating performance analysis work of impeller and marking it impossible to obtain an accurate result (characteristic numerical value) due to performance analysis by way of various turbulence modeling.
The present invention is disclosed to solve the aforementioned problems and it is an object of the present invention to provide a performance analysis method of centrifugal impeller adapted to simplify performance analysis of impeller and to obtain an accurate calculation result in comparison with analysis by way of averaging the entire flow of the centrifugal impeller.
In accordance with the object of the present invention, there is provided a performance analysis method of centrifugal impeller, the method for measuring a flow field at an impeller exit to analyze an exit flow angle, total pressure ratio and efficiency, thereby enabling to analyze performance of the manufactured centrifugal impeller, wherein the flow field of the centrifugal impeller at the impeller exit is dualized into a jet region flow field and a wake region flow field, by which each flow field thereof is sought and averaged to obtain the flow field.